Tagged Questions

In number theory, a multiplicative function is a function defined
on positive integers such that f(ab)=f(a)f(b) for a,b coprime.
E.g. Euler's totient function, sum of divisors and number of
divisors are multiplicative functions.

In a numerical experiment I notice for sum moduli $N$ there are much less than $N/2$ perfect squares. I had chosen a large number, the simplest example is $N=8$.
Using the Chinese Remainder Theorem ...

$\lambda(n)$= $\sum_{d^2|n}$ $\mu(n/d)^2$
and $\mu^2(n)$= $\sum_{d^2|n}$ $\mu(d)$
Having a little bit of trouble here.Can I use the fact that $\sum_{d|n}\lambda(n)$ is a characteristic function for ...

I have a multiplicative function $f$ with a special "base" case: For every prime $p$, $f(p) = 1$. E.g. splitting up $f(3^5 \times7^2 \times 13 \times 17)$ yields $f(3^5) f(7^2)$ which is left to be ...

How can I prove:
$$\sum \limits_{d|n}(n/d)\sigma(d) = \sum \limits_{d|n}d\tau(d)?$$
Few observations :
Left side is a sum function and the right side is a number of divisors function. Both the sides ...

I'm studying algebra, and I came across some questions on multiplicative functions (that should be number theory though?). One is: prove that mobius function is multiplicative. But I've not been given ...

Ok, I obviously understand basic multiplication and understand why those don't equal. But in web colors, therr is FFFFFF hexadecimal different colors (or rather $16,777,215$ in base $10$). This amount ...

show that
$$\sum_{t|n}(d(t))^3=\left(\sum_{t|n}d(t)\right)^2$$
where $d(n)$ is the number of positive divisors of $n$.
see this have simaler
$$1^3+2^3+\cdots+n^3=\left(1+2+\cdots+n\right)^2$$
maybe ...